Universal Safety for Timed Petri Nets is PSPACE-complete

TL;DR

This paper proves that the universal safety problem for controller-less timed networks, modeled as timed automata, is PSPACE-complete, establishing its computational complexity and duality with coverability in timed-arc Petri nets.

Contribution

It introduces the universal safety problem for timed networks and proves its PSPACE-completeness, connecting it to the existential coverability problem in timed-arc Petri nets.

Findings

Universal safety for timed networks is PSPACE-complete.

The problem is dual to the existential coverability problem.

Complexity results apply to arbitrary-sized networks.

Abstract

A timed network consists of an arbitrary number of initially identical 1-clock timed automata, interacting via hand-shake communication. In this setting there is no unique central controller, since all automata are initially identical. We consider the universal safety problem for such controller-less timed networks, i.e., verifying that a bad event (enabling some given transition) is impossible regardless of the size of the network. This universal safety problem is dual to the existential coverability problem for timed-arc Petri nets, i.e., does there exist a number $m$ of tokens, such that starting with $m$ tokens in a given place, and none in the other places, some given transition is eventually enabled. We show that these problems are PSPACE-complete.